光刻调焦调平测量系统算法比较研究

调焦调平测量系统是光刻机对焦控制的核心部件,调焦调平测量系统的数据处理精度影响光刻机的对焦控制性能,计算速度影响光刻机产能。论文通过仿真与实验对比分析了多项式拟合算法(polynomial fitting)、RF(random forest)算法和XGBoost(extreme gradient boosting)算法在调焦调平测量系统中的测量精度与计算耗时。仿真与实验结果表明,多项式拟合算法精度随时间变化不敏感,RF算法和XGBoost算法精度随计算时间的增加而迅速提升。对于不存在噪声的仿真数据,7阶多项式拟合的3σ值为0.001nm;RF算法在2ms时可对仿真数据完全拟合;XFBoost算法在5ms时,拟合精度基本趋于稳定,为0.6nm。对于存在噪声的实验数据,RF算法与XGBoost算法对噪声有较好的鲁棒性,随计算时间的增加,RF算法与XGBoost算法拟合精度不断提升并分别于3ms和5ms超越多项式拟合算法,但精度提升有限。在光刻机中,为了兼顾对焦精度和产能,必须兼顾算法的拟合精度与拟合时间,因此调焦调平测量系统选用多项式拟合算法较为合适。

Comparative Study on Algorithms of Focusing and Levelling Measurement System in Lithographic Tool

Focusing and levelling measurement system is the core component for focus control in the lithographic tool.The da?ta processing accuracy of the measurement system affects the focus control performance of the lithographic tool and the calculation speed affects throughput.This paper compares the measurement accuracy and computational time of the polynomial fitting,RF(ran?dom forest)algorithm and XGBoost(extreme gradient boosting)algorithm in the focusing and levelling measurement system by sim?ulation and experiment.Simulation and experimental results show that the accuracy of polynomial fitting algorithm is less sensitive with time,and RF algorithm and XGBoost algorithm increases rapidly with the increase of computation time.For simulation data without noise,the 3σvalue of the 7th order polynomial fitting algorithm is 0.001 nm,RF algorithm can completely fit the simula?tion data after 2ms,and XFBoost algorithm is basically stable at 0.6nm after 5ms.For experimental data with noise,RF algorithm and XGBoost algorithm are robust to noise.With the increase of calculation time,the fitting accuracy of RF algorithm and XGBoost algorithm is continuously improved and surpass that of the polynomial fitting algorithm in 3ms and 5ms respectively,but the accura?cy improvement is limited.In order to balance the focusing accuracy and productivity in the lithographic tool,the fitting accuracy and fitting time of algorithms must be considered simultaneously.Therefore,the polynomial fitting algorithm is more suitable for the focusing and levelling measurement system.